In the interest of eliminating visible smoke emissions from escaping into the surrounding atmosphere from domestic barbecue grills it has been established that such grills may be provided with smokestacks having an afterburner means associated therewith which structure is effective to ignite and burn these solid particles which are a part of the stream of effluent flowing from the cooking process and are the source of the visible pollutants. As these visible smoke particles and other combustible material in the effluent burn, these formerly visible pollutants and other combustible products are converted into invisible gaseous compounds within the emissions that flow from the stack. A known structure and method for accomplishing this desired result is shown in my issued U.S. Pat. Nos. 5,226,402 and 5,357,940.